CN109948567B - Graph theory-based gas-liquid two-phase flow pattern identification method for long-distance water delivery system - Google Patents
Graph theory-based gas-liquid two-phase flow pattern identification method for long-distance water delivery system Download PDFInfo
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Abstract
A method for identifying a gas-liquid two-phase flow pattern of a long-distance water delivery system based on graph theory belongs to the technical field of water supply safety analysis of the long-distance water delivery system, and can identify the gas-liquid two-phase flow pattern. Firstly, extracting a pressure signal to obtain a time sequence curve, dividing the time sequence curve into a plurality of windows according to the width of a peak on the time sequence curve, taking the average value of the pressure signal values in each window as a node, and reordering the windows in a descending order or an ascending order according to the size. Secondly, a complex network graph is constructed according to whether the nodes generate connection or not. And finally, reflecting the flow pattern change trend according to the statistical characteristics of the complex network structure chart. The method does not need expensive experimental monitoring equipment and complex pressure signal processing technology, can simply and intuitively judge the gas-liquid two-phase flow pattern in the real water conveying pipeline (opaque pipeline) in a graph theory mode, can predict the flow pattern change trend according to quantitative dynamic characteristics of some indexes, and provides guiding significance for the safe operation of the water conveying pipeline.
Description
Technical Field
The invention belongs to the field of water supply safety analysis of a long-distance water delivery system, relates to a method for identifying a gas-liquid two-phase flow pattern of a water delivery pipeline, and particularly relates to a method for identifying a gas-liquid two-phase flow pattern of a long-distance water delivery system based on graph theory.
Background
The retention of gas in a water supply pipeline is a common phenomenon, and the flow rule of gas-water two-phase flow caused by the retention has important significance for the safe operation of the water supply pipeline. With the development of urbanization in China, the water demand of cities is increasing continuously. Long-distance water delivery projects from areas with abundant water resources to cities can be used for relieving the water supply pressure of water-deficient cities. However, in long-distance water pipelines, two-phase flow of gas and water generated by gas retention is common. The existence of gas and water two-phase flow makes pipeline pressure and hydraulic conditions become complicated and changeable, can reduce water delivery capacity, increases head loss, causes pipeline vibration and even can lead to the pipe explosion accident. And the pipe explosion accident often causes great economic loss. Therefore, it is necessary to pay attention to the safe operation of the water pipeline, and the flow pattern is used as an important parameter of the gas-water two-phase flow, and the change of the flow pattern can reflect the hydraulic transition process of the pipeline to a certain extent.
However, most current flow pattern identification methods are not suitable for long distance water pipelines. Most of the existing methods, such as phase density imaging, electrical resistance tomography, etc., tend to be very costly. And the long-distance water conveying pipeline has a long distance, a plurality of parts needing to be monitored are arranged, and most pipelines are buried underground. Therefore, from the aspect of cost performance, the flow pattern identification based on the pressure signal obtained at the pressure sensor is more in line with the real requirement. In the water supply pipeline, the gas content can be roughly divided into 4 types of bubble flow, slug flow, reverse flow and stratified flow according to the difference of the gas content (from low to high). Wherein, the bubble flow is a normal flow state under a safe operation state, and the tube explosion probability is obviously increased when the reverse airflow and the stratified flow are carried out. The method for processing the pressure signals is provided, and the flow pattern type is intuitively and clearly shown in a graph theory mode, so that the method has important significance for identifying the flow pattern of the opaque long-distance water pipeline and taking certain safety measures.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for identifying the gas-liquid two-phase flow pattern of a long-distance water delivery system based on graph theory.
The purpose of the invention can be realized by the following technical scheme:
a method for identifying the flow pattern of gas-liquid two-phase flow of a long-distance water delivery system based on graph theory is used for realizing the process of identifying the flow pattern of the gas-liquid two-phase flow according to the following steps:
(1) signal extraction and preprocessing
The pressure signal is obtained from a pressure sensor on the pressure pipeline, and the obtained pressure signal graph is a time series curve. Dividing the time series curve into a plurality of windows according to the width of the wave crest on the time series curve, calculating the average value of the pressure signal value in each window, wherein each average value is a node, and each average value is used as the characteristic value of each corresponding node in the complex network. And carrying out descending or ascending reordering on each node according to the corresponding average value, wherein the nodes after descending reordering correspond to the gas-containing rates reflected in the corresponding pressure signal sections from front to back from small to large, and the nodes after ascending reordering correspond to the gas-containing rates reflected in the corresponding pressure signal sections from front to back from large to small. Since gas and water have different effects on the pressure signal. When the gas content is higher, the pressure signal value is reduced. Therefore, the change of the gas content in the gas-liquid two-phase flow can be reflected according to the rising and falling trend of the pressure signal value.
(2) Constructing and analyzing a complex network structure graph
And constructing a complex network graph according to whether the nodes generate connection or not. And (3) according to the reordered nodes, randomly selecting the node (i) and the node (j), and judging whether the connection is generated between the node (i) and the node (j) according to the following formula:
Dij＝|M(i)-M(j)|,0≤i≠j≤n (1)
wherein, m (i) represents the average value corresponding to the node (i), m (j) represents the average value corresponding to the node (j), and n represents the number of generated nodes. When E is represented by the formula (2)ijWhen the value is 1, the node (i) and the node (j) are connected; when E isijAt 0, node (i) and node (j) are not connected. And the coefficient a is used for ensuring the reasonability and robustness of the complex network calculation result, and the coefficient a takes a natural number between 0 and 1, and similar results can be generated when the value is in the neighborhood of a. And each gas-water two-phase flow pattern corresponds to a similar complex network diagram.
The influence of gas and water in the gas-water two-phase flow in the pipeline on the pressure signal is different, and when the gas content is more, the pressure signal value is reduced. Therefore, from the results of the pressure signal preprocessing (taking the example of node reordering as descending processing), it can be seen that the gas content is lower as the node tag number is higher, and the pressure signal corresponding to the node tag number later reflects that the gas content in the gas-water two-phase flow is higher. Based on this fact, assume that: the nodes in front of the label number may represent water elements and the nodes in the back of the label number may represent gas elements. According to the assumption, the physical significance of the gas-liquid two-phase flow pattern in the water delivery system displayed by a complex network diagram is analyzed.
For stratified flow, the gas is gathered at the upper layer of the pipeline due to the high gas content in the water pipeline, so that obvious stratification phenomenon occurs between the gas and the water flow at the bottom of the pipeline. Therefore, the average value difference between the nodes with the front labels and the nodes with the back labels in the n nodes formed by the pressure signals is large, the complex network formed by hierarchical flow is loose, the connection among the nodes is small, and the average value difference between the nodes with the back labels is small due to the large gas content, and the community size formed by the nodes with the lowest labels is the largest. For the reverse gas flow, although the higher gas content is not enough to form the stratified flow, the formed gas mass is larger in size, compared with the stratified flow, although the average value difference between the nodes at the front of the label number and the nodes at the back of the label number is still larger, the connection between the nodes forming the complex network structure is strengthened, the community size formed by the nodes at the back of the label number is reduced, and in addition, the connection between communities is also compact, which shows that the average value difference between the whole complex network becomes smaller along with the reduction of the gas content. Slug flow is a flow pattern with a pipeline gas content lower than that of counter-current gas flow, under the prevailing condition, the connection between nodes (including nodes in the same community and nodes between different communities) is further strengthened, and the community size formed by nodes with the most back label numbers is further reduced. As for the bubble flow with the minimum gas content, the gas is dispersed in the water flow as tiny bubbles or dissolved in the water flow, so that the mutual difference among the nodes of the whole complex network is minimum, and the overall structure of the complex network is the most compact due to the close connection among the nodes.
(3) Reflecting flow pattern change trend according to statistical characteristics of complex network structure diagram
According to the complex network diagram, the flow pattern characteristics of the gas-liquid two-phase flow in the real water conveying pipeline can be visually represented in a graph theory mode. The variation trend of the flow pattern can be predicted according to the dynamic variation characteristics of the specific flow pattern. The modularity Q, the graph density G and the average path length l can be utilizedGThree indexes are used for analyzing the evolution trend of the flow pattern respectively.
First, using the modularity Q, the graph density G, and the average path length lGThe statistical characteristics of the complex network graph corresponding to each flow pattern are quantitatively analyzed by three indexes, and the statistical characteristics are calculated according to the following formulas respectively:
wherein if node (i) and node (j) make a connection, AijIs 1. If node (i) and node (j) do not make a connection, AijIs 0.
The number of all connections generated in the entire complex network; n is the total number of nodes generated. k is a radical ofi＝∑jAijRepresenting the total number of connections, k, associated with node (i)j＝∑iAijRepresenting the total number of connections associated with node (j). c. CiIs the community in which node (i) is located, cjIs the community in which the node (j) is located, if the node (i) and the node (j) belong to the same community, delta (c)i,cj) Is 1. If node (i) and node (j) do not belong to the same community, δ (c)i,cj) Is 0. D (n) when node (i) and node (j) are not connectedi,nj) Is 0, when node (i) and node (j) are directly connected, d (n)i,nj) Is 1. D (n) when node (i) and node (j) are not directly connected but can be mediated by other nodesi,nj) For the shortest path length from node (i) to node (j), each time via a connection d (n)i,nj) Plus 1.
As the air content changes from large to small, the flow pattern is transited by stratified flow, inverse air flow, slug flow and bubble flow in turn. Meanwhile, the structure of a complex network diagram reflecting gas-liquid two-phase flow is changed from loose to compact, the connection among communities formed by nodes is also changed to compact, and the possibility of generating connection among the nodes is continuously increased. Correspondingly, the modularity Q for measuring the community division quality is in a descending trend, the complex network with a compact structure enables the graph density G to be in an increasing trend, the node connection possibility is increased, the path length l between the nodes is reduced, and the average path length l of the whole complex network is smallerGWith a decreasing trend. The evolution trend of the flow pattern can be predicted based on the quantitative change characteristics of the three indexes in a certain time.
Compared with the prior art, the invention has the beneficial effects that: expensive experimental monitoring equipment and complex pressure signal processing technology are not needed, the gas-liquid two-phase flow pattern in the real water conveying pipeline (opaque pipeline) can be simply and visually judged in a graph theory mode, the flow pattern change trend can be predicted according to quantitative dynamic characteristics of some indexes, and guiding significance is provided for safe operation of the water conveying pipeline.
Drawings
FIG. 1 is a diagram of an experimental setup for an experimental piping loop; in the figure: the system comprises a water tank 1, a pump 2, an electric control valve 3, a pneumatic butterfly valve 4, an ultrasonic flowmeter 5, an air inlet 6, a pressure sensor 7, a gas rotameter 8, an air compressor 9, a data acquisition instrument 10 and a computer 11.
FIG. 2 is a schematic diagram of a time series division window of a pressure signal; wherein the window is 400 and the step size is 350.
FIG. 3 is a photograph of an experiment showing 4 typical flow regimes; (a) is a bubble flow, (b) is a slug flow, (c) is a counter-current flow, and (d) is a stratified flow.
FIG. 4 is a time series of pressure signals for 4 exemplary flow regimes selected; (a) is a stratified flow, (b) is a counter-current flow, (c) is a slug flow, and (d) is a bubble flow.
FIG. 5 is a complex network diagram corresponding to 4 exemplary flow regimes; from left to right, laminar flow, reverse airflow, slug flow and bubble flow are sequentially carried out.
FIG. 6(a) is the evolution characteristics of the flow regime change of the modularity index along with the change of the gas fraction (the time series division of the pressure signal is that the window is 400 and the step length is 350); FIG. 6(b) is the evolution characteristics of the change of flow regime with the change of gas void ratio, which is an index of the graph density and the average path length (time series division of the pressure signal: window is 400, and step length is 350);
FIG. 7(a) is the evolution characteristics of the flow regime change of the modularity index with the change of the gas fraction (time series division of the pressure signal: window 440, step 391); FIG. 7(b) is the evolution characteristics of the change of flow regime with the change of gas fraction for the indicators of map density and average path length (time series division of pressure signal: window 440, step 391); FIG. 7(c) is the evolution characteristics of the flow regime change of the modularity index with the change of the gas fraction (time series division of the pressure signal: window is 350, step length is 333); FIG. 7(d) is a graph showing the evolution of flow regime change with respect to change in gas cut for the graph density and average path length (time series division of pressure signal: window 350, step 333).
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples, but the embodiments of the invention are not limited thereto. A water supply line case was chosen to illustrate the effectiveness of the process. The specific implementation steps are as follows:
(1) signal extraction and preprocessing
The experimental setup of the water supply pipeline is shown in fig. 1: the specific structure is described as follows: the bottom of the water tank 1 is connected with two ends of a pipeline, the total length of the pipeline is 80m, the pipeline is made of organic glass, and the outer diameter and the inner diameter of the pipeline are 110mm and 90mm respectively. The pipeline connected with one side of the water tank 1 is a horizontal section, and is sequentially provided with a pump 2, an electric control valve 3, a pneumatic butterfly valve 4, an ultrasonic flowmeter 5 and an air inlet 6; the air inlet 6 is connected with an air compressor 9 through a pipeline, and a gas rotameter 8 is arranged on the pipeline; the electric control valve 3 and the ultrasonic flowmeter 5 are both connected with a computer 11 through a data acquisition instrument. The other end of the pipeline is a horizontal pipe section, an inclined ascending pipe section, a horizontal pipe section, an inclined descending pipe section and a horizontal pipe section in sequence. And the inclined ascending pipe section is provided with a pressure sensor 7 and is a measured pipe section. The inclined ascending and inclined descending pipe sections and the horizontal pipeline between the inclined ascending and inclined descending pipe sections are required to be perpendicular to the horizontal plane of the rest pipe sections, and the angle between the inclined ascending and inclined descending pipe sections and the horizontal plane is 45 degrees. The function of the pump 2 is to maintain the cyclic movement of the experimental device fluid. The air compressor 9 injects air into the pipeline, the air flow is controlled by the pneumatic butterfly valve 4, and the accurate value is obtained by the air rotameter 8. The water flow is controlled by an electric control valve 3, and an accurate value is obtained by an ultrasonic flowmeter 5. The pressure signal is obtained by a pressure sensor 7. The measurement accuracy of the pressure sensor is 0-200kPa, and the accuracy is 0.2%. The high-speed camera is arranged on the side surface of the whole experimental device and is used for photographing the gas-liquid two-phase flow of the measured pipe section (the downward inclined pipe section where the pressure sensor is located).
The experimental process comprises the following steps:
1) the gas flow rate was fixed at 4.0m3The flow rate of the water body changes from small to large to reach various target values (0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 and 2.7 m/s).
2) The sampling frequency of the pressure signal is 1kHz, and each sampling time is 20 s.
3) The gas-liquid two-phase flow of the measured pipe section (the downward inclined pipe section where the pressure sensor is located) is photographed by a high-speed camera arranged on the side surface.
According to the experimental process, pressure signal time sequence data under 16 different gas and liquid flow parameters are obtained. The total length of each time series is 20000. In the following, taking a pressure signal of a certain gas and liquid flow rate part as an example, a signal preprocessing before constructing a complex network structure by using pressure signal time series data is described as shown in fig. 2, in this example, a window and a step length are selected to be 400 and 350, respectively (actually, the window and the step length are not fixed, and can be set reasonably according to the fluctuation characteristics of the pressure signal).
The pressure signal preprocessing specification is as follows:
1) since the window size introduced is 400, data points between 0-400 are first truncated as a window. The step size introduced is 350, so after each window is determined, the next window contains data points that were determined by shifting the original window to the right by 350. So, the second window contains data points between 350-. Therefore, the time series of pressure signals obtained under certain gas and liquid flow conditions can be divided into 57 such windows.
2) And calculating the overall average value of all data points in each window, wherein each average value is used as the characteristic value size of each corresponding node in the complex network.
3) All the calculated averages are reordered in descending order so that the node tag number for the window with the largest average is 1 and the node tag numbers for windows with smaller averages are later.
4) The robustness of the complex network graph is further verified by introducing two modes of a window 440, a step 391, a window 350 and a step 333 according to the same method.
(2) Construction and analysis of complex network structure diagrams
Selecting gas and liquid flow parameters of "4.0-0.7", "4.0-1.1", "4.0-1.9" and "4.0-2.7" (taking "4.0-0.7" as an example, representing a gas flow of 4.0m3Flow velocity of water body of 0.7m/s) as typical examples of stratified flow, counter-current flow, slug flow, bubble flow, respectively, and the corresponding pressure signal time series are shown in fig. 4.
The complex network structure of 4 typical flow patterns is constructed according to the formulas (1) and (2) in the summary of the invention, and the result is shown in fig. 5.
The influence of gas and water in the gas-water two-phase flow in the pipeline on the pressure signal is different, and when the gas content is more, the pressure signal value is reduced. Therefore, from the result of the pressure signal preprocessing, it can be known that the gas content is lower as the node label number is closer, and the gas content in the gas-water two-phase flow is reflected by the pressure signal corresponding to the node label number which is later. Based on this fact, an assumption can be made that: the nodes in front of the label number may represent water elements and the nodes in the back of the label number may represent gas elements. Based on this assumption, the physical meaning reflected by the 4 complex network structure diagrams can be analyzed.
Hierarchical flow Complex structured network As shown in FIG. 5(a), community C1 contains 0-23 nodes, community C2 contains 24-39 nodes, and community C3 contains 40-52 nodes. While nodes 53-56 are difficult to connect to community C3 because the gas ratio of these 4 nodes is particularly high. In addition to these 4 nodes, the gas content of the node belonging to community C3 is the largest compared to community C1 and community C2. In addition, there is little connection between community C3 and community C2. Nodes in the same community have similar gas contents, and the average value difference of the nodes is not large, which means that more connections are generated between the nodes. And the gas content between nodes belonging to different communities is greatly different, so that the connection is less. Community C3 may indicate the presence of gas pockets in a gas-liquid two-phase flow, while community C1 may indicate a bottom flow with less dissolved gas in a gas-liquid two-phase flow, since the node attributed to community C1 has the lowest gas content.
The complex network of the counter-current flow is shown in fig. 5(b), which is similar to the complex network of the stratified flow. The difference between the flow pattern and the stratified flow is mainly shown in the following two aspects: the number of free nodes behind communities C3 and C3 is reduced, namely the number of nodes with higher gas content is reduced, which means that the content of gas volume in gas-liquid two-phase flow is reduced, and the situation is consistent with the fact that the air bag is reduced because the flow rate of water body is increased when the gas flow is kept unchanged. ② the connection between adjacent communities (especially communities C3 and C2) is enhanced. This means that the corresponding mean difference between the nodes belonging to the two communities becomes smaller and the water and gas elements become more compatible. The connection between community C1 and community C2 also becomes stronger compared to the case of stratified flow, indicating that as the flow velocity of the water stream increases, the shear force increases and the ability of the gas to dissolve in the water body becomes stronger.
The complex structure network of slug flow is shown in fig. 5(c), which is a flow pattern generated by further increasing the flow velocity of the water body. The connection between adjacent communities is further strengthened, the strengthened connection between communities C2 and C1 shows that the gas dissolving capacity of the water body is strengthened, and the strengthened connection between communities C3 and C2 shows that the possibility of air bag accumulation is lowered. In addition, the number of nodes attributed to community C3 is further reduced, which also demonstrates the smaller size of the air bags in this flow regime compared to stratified and counter-current flow.
The bubble flow complex structure network is shown in fig. 5(d), which is the final result of the air bag size decreasing with the increasing water flow speed, that is, the air injected by the air compressor is dissolved or dispersed in the water flow uniformly, forming a large amount of micro bubbles. The disappearance of the community C3 shows that no air bags appear in the gas-liquid two-phase flow, the connection between the communities C1 and C2 is extremely compact, and the strong interweaving between the micro bubbles and the water flow is shown, so that the difference between the nodes belonging to the two communities is not obvious. Note that nodes 0 and 1 are free outside of community C1 because their gas content is extremely low, making the difference from nodes within community C1 large.
(3) Complex network statistical property analysis
Three indicators of the complex network (modularity, graph density and mean path length) were generated from the pressure signal time series in all cases during the experiment, and the approximate evolution trend of these 4 flow patterns was analyzed from a statistical point of view. The results are shown in FIG. 6.
Modularity: overall, the modularity of the complex network tends to decrease in the evolution from stratified flow to bubble flow. Because the gas content is reduced along with the increase of the water flow rate, the difference between the nodes is reduced, so that more connections can be established between the nodes of different communities, which is consistent with the result of fig. 5, and the negative influence on the community division quality is generated. The modularity therefore tends to decrease. Since the calculation of the modularity is inherently an optimization process, it is normal that some of the data points deviate from the downward trend, so that the entire curve is jagged. In order to ensure the rationality of the result of the generated complex network structure, in some cases, the coefficient a is selected slightly differently, which is another reason for the non-flat descending curve.
Graph density and average path length: as can be seen in fig. 6, as the gas content of the gas-liquid two-phase flow of the pipe decreases, the graph density of the entire complex network increases, while the average path length of 57 nodes decreases. From the plot, the mean path length of stratified flow is longest (greater than 3.5), while the plot density of bubble flow is greatest (close to 0.6). These trends can be attributed to two reasons: firstly, because of the reduction of the gas content, the air bag in the pipeline becomes small until the air bag disappears; and secondly, with the increase of the flow velocity of the water body, the shearing force of the water flow is enhanced, and the capability of dissolving and dispersing the gas in the water body is enhanced. In addition, the coefficient a is selected to influence the smoothness of the graph density and the average path length curve, but the overall trend is not influenced.
In the construction process of a complex network, different windows and step lengths are selected, and the number of obtained nodes is different. The previous example is a window of 400 and a step size of 350. Window 440, step 391 and window 350, step 333 are now selected to build a new complex network (the result is shown in fig. 7). In the three cases, the obtained node numbers are 57, 51 and 60 respectively, and the repetition degrees of the pressure signal sections corresponding to the adjacent nodes are 0.125, 0111 and 0.057 respectively. Comparing fig. 6 and 7, it can be seen that the trends in the evolution of the modularity, map density and average path length are consistent. The result shows that the complex network result has robustness within a certain range of window and step size.
In conclusion, by using the method for judging the gas-liquid two-phase flow pattern of the long-distance water delivery system based on the graph theory (complex network), the judgment of the gas-liquid two-phase flow pattern in the water supply pipeline and the judgment of the flow pattern evolution trend can be realized, and guidance is provided for a decision maker to ensure the safe operation of the water supply pipeline.
The above-mentioned embodiments only express the embodiments of the present invention, but not should be understood as the limitation of the scope of the invention patent, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the concept of the present invention, and these all fall into the protection scope of the present invention.
Claims (1)
1. A method for identifying a gas-liquid two-phase flow pattern of a long-distance water delivery system based on graph theory is characterized by comprising the following steps of:
(1) signal extraction and preprocessing
Acquiring a pressure signal from a pressure sensor on a pressure pipeline, wherein the obtained pressure signal graph is a time series curve; dividing the time series curve into a plurality of windows according to the width of the wave crest on the time series curve, and calculating the average value of pressure signal values in each window, wherein each average value is used as a node; reordering each node in a descending or ascending order according to the corresponding average value, wherein the nodes after descending order rearrangement correspond to the gas-containing rates reflected in the corresponding pressure signal sections from small to large from the front to the back, and the nodes after ascending order rearrangement correspond to the gas-containing rates reflected in the corresponding pressure signal sections from large to small from the front to the back; reflecting the gas content change in the gas-liquid two-phase flow according to the rising and falling trend of the pressure signal value;
(2) constructing and analyzing a complex network structure graph
Constructing a complex network graph according to whether the nodes generate connection or not; and (3) according to the reordered nodes, randomly selecting the node (i) and the node (j), and judging whether the connection is generated between the node (i) and the node (j) according to the following formula:
Dij＝|M(i)-M(j)|,0≤i≠j≤n (1)
wherein, m (i) represents an average value corresponding to the node (i), m (j) represents an average value corresponding to the node (j), and n represents the number of generated nodes; when E is represented by the formula (2)ijWhen 1, node (i) and node (j) generateConnecting; when E isijWhen 0, node (i) and node (j) are not connected; the coefficient a is used for ensuring the reasonability and robustness of a complex network calculation result, and similar results can be generated when a natural number between 0 and 1 is taken and taken in the neighborhood of a; each gas-water two-phase flow pattern corresponds to a similar complex network diagram;
(3) reflecting flow pattern change trend according to statistical characteristics of complex network structure diagram
The complex network diagram can intuitively represent the flow pattern characteristics of gas-liquid two-phase flow in a real water conveying pipeline in a graph theory mode; the change trend of the flow pattern can be predicted according to the dynamic change characteristics of the specific flow pattern; using modularity Q, graph density G, and average path length lGThree indexes respectively analyze the evolution trend of the flow pattern:
first, using the modularity Q, the graph density G, and the average path length lGThe statistical characteristics of the complex network graph corresponding to each flow pattern are quantitatively analyzed by three indexes, and the specific formula is as follows:
wherein if node (i) and node (j) make a connection, AijIs 1; if node (i) and node (j) do not make a connection, AijIs 0;
the number of all connections generated in the entire complex network; n is the total number of nodes generated; k is a radical ofi＝∑jAijRepresenting the total number of connections, k, associated with node (i)j＝∑iAijRepresents the total number of connections associated with node (j); c. CiIs the community in which node (i) is located, cjIs the community in which the node (j) is located, if the node (i) and the node (j) belong to the same community, delta (c)i,cj) Is 1; if node (i) and node (j) do not belong to the same community, δ (c)i,cj) Is 0; d (n) when node (i) and node (j) are not connectedi,nj) Is 0, when node (i) and node (j) are directly connected, d (n)i,nj) Is 1; d (n) when node (i) and node (j) are not directly connected but can be mediated by other nodesi,nj) For the shortest path length from node (i) to node (j), each time via a connection d (n)i,nj) Plus 1.
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